Simplify cube root of (32x^12y^3)/(4x^3)

$\sqrt[3]{\frac{32 x^{12} y^{3}}{4 x^{3}}}$

Reduce the expression $\frac{32 x^{12} y^{3}}{4 x^{3}}$ by cancelling the common factors.

Factor $4$ out of $32 x^{12} y^{3}$ .

$\sqrt[3]{\frac{4 (8 x^{12} y^{3})}{4 x^{3}}}$

Factor $4$ out of $4 x^{3}$ .

$\sqrt[3]{\frac{4 (8 x^{12} y^{3})}{4 (x^{3})}}$

Cancel the common factor.

$\sqrt[3]{\frac{4 (8 x^{12} y^{3})}{4 x^{3}}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{12} y^{3}}{x^{3}}}$

Cancel the common factor of $x^{12}$ and $x^{3}$ .

Factor $x^{3}$ out of $8 x^{12} y^{3}$ .

$\sqrt[3]{\frac{x^{3} (8 x^{9} y^{3})}{x^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{3} (8 x^{9} y^{3})}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{3} (8 x^{9} y^{3})}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{9} y^{3}}{1}}$

Divide $8 x^{9} y^{3}$ by $1$ .

$\sqrt[3]{8 x^{9} y^{3}}$

Rewrite $8 x^{9} y^{3}$ as ${(2 x^{3} y)}^{3}$ .

$\sqrt[3]{{(2 x^{3} y)}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$2 x^{3} y$